It's masculine nominative singular.
The possessive pronoun (that stands alone, e.g. "mine" in English) has a slightly different set of endings from the possessive determiner (that stands before a noun, e.g. "my" in English). Perhaps you're looking at those?
mein Hund (determiner) but meiner (pronoun).
Ah, the nuances of language! "Larger" and "bigger" are not always interchangeable. Should I be talking to two teenage girls one of which was taller than the other, I might say "Sally is bigger than you" and it would be ok to say but not exactly the correct usage. However....don't ever say "Sally is larger than you" as it might cause the "taller" girl to be quite hurt. :)
Because it's a possessive pronoun (standing instead of a noun) rather than a possessive determiner (standing before a noun). Those inflect slightly differently, and have endings for masculine and neuter nominative as well as neuter accusative.
dein Hund but deiner
Compare English, where we say "your dog" but "yours" -- the pronoun is a bit longer than the determiner.